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| Autor/in | Plaxco, David |
|---|---|
| Titel | Relating Understanding of Inverse and Identity to Engagement in Proof in Abstract Algebra |
| Quelle | (2015), (399 Seiten)
PDF als Volltext Ph.D. Dissertation, Virginia Polytechnic Institute and State University |
| Sprache | englisch |
| Dokumenttyp | gedruckt; online; Monographie |
| ISBN | 978-1-3697-26619 |
| Schlagwörter | Hochschulschrift; Dissertation; Mathematics Instruction; Mathematical Logic; Validity; Interviews; Algebra; Coding; Mathematical Concepts; Correlation; Concept Formation; Grounded Theory |
| Abstract | In this research, I set out to elucidate the relationships that might exist between students' conceptual understanding upon which they draw in their proof activity. I explore these relationships using data from individual interviews with three students from a junior-level Modern Algebra course. Each phase of analysis was iterative, consisting of iterative coding drawing on grounded theory methodology (Charmaz, 2000, 2006; Glaser & Strauss, 1967). In the first phase, I analyzed the participants' interview responses to model their conceptual understanding by drawing on the form/function framework (Saxe, et al., 1998). I then analyzed the participants proof activity using Aberdein's (2006a, 2006b) extension of Toulmin's (1969) model of argumentation. Finally, I analyzed across participants' proofs to analyze emerging patterns of relationships between the models of participants' understanding of identity and inverse and the participants' proof activity. These analyses contributed to the development of three emerging constructs: form shifts in service of sense-making, re-claiming, and lemma generation. These three constructs provide insight into how conceptual understanding relates to proof activity. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.] (As Provided). |
| Anmerkungen | ProQuest LLC. 789 East Eisenhower Parkway, P.O. Box 1346, Ann Arbor, MI 48106. Tel: 800-521-0600; Web site: http://www.proquest.com/en-US/products/dissertations/individuals.shtml |
| Erfasst von | ERIC (Education Resources Information Center), Washington, DC |
| Update | 2020/1/01 |
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